Some parts are easy to match, made in known models by known makers. Matching antique hardware that was never cataloged is a different job, and real detective work. It's the hardest and most satisfying part of the trade.
Identify first
A great deal of old hardware and lighting was made before or outside standardization, by countless small manufacturers turning out their own patterns. There's no master catalog for all of it, no part number to look up, so when you need to match a fitting with no documented model, you can't order the same one. You have to identify what it is by its own evidence. The material, the method (forged, cast, stamped), the finish, the style and its period, the dimensions, the maker's marks if any, all of it narrows the field. An experienced eye reads those clues and places a part in a time, a region, and often a manufacturer, even without a catalog.
Then hunt
Matching an uncataloged part means knowing the field, the makers, the patterns, the period conventions, well enough to recognize a match when it surfaces, and having the inventory and the network to find one. It's knowledge and patience more than luck, though luck helps. This is where a specialist earns the name: a general store can't match an uncataloged fitting, but a dealer who has handled thousands of them often can.
Salvager's Note: For an uncataloged part, send a clear photo and a measurement. Those two things let a specialist read the material, method, and period, place the part, and tell you whether a match exists, which no catalog search can do for hardware that was never in one.